Bring 4 cups water to a boil in a medium saucepan. Add tea bags, and let steep for 5 minutes.
Place strawberries in a bowl. Bring water and sugar to a boil in a small saucepan, stirring until sugar dissolves. Remove from heat, add basil, and let steep for 10 minutes. Strain over strawberries; discard basil. Toss to coat. Let stand until cool, about 25 minutes. Combine strawberries (with syrup) and tea in a pitcher. Refrigerate until chilled. Serve over ice, and garnish with basil.